Fairfax, Va. ? Police said Monday that a Virginia man who killed four people, then himself, on Christmas Day had a history of mental problems.

Still, police were trying to determine a motive for the rampage. “Perhaps we’ll never be able to answer the question that is most prevalent, and that is why,” said Col. David Rohrer, chief of the Fairfax County, Va., Police Department.

“This is obviously a complex investigation with separate crime scenes and five victims. The events … have certainly shocked and saddened us all,” Rohrer said.

Investigators believe Nathan W. Cheatham shot and killed his mother in the driveway of her McLean home. He then drove 10 miles to a home in Great Falls and fired more than 50 shots that killed three other people, before turning the gun on himself.

Cheatham, 27, had been arrested on several occasions by Fairfax County police for what they described as “minor infractions.”

He had been living with his mother, Sheila G. Cheatham, 53, for at least two weeks. He had also stayed with his two brothers at another location in Fairfax County. Police are hoping they can learn some indication of his demeanor, which may lead to an understanding of what led him to go on a rampage.